Solve (1-2/3)^2+sqrt{1-7/8}-11/18

$$( 1 - \frac { 2 } { 3 } ) ^ { 2 } + \sqrt { 1 - \frac { 7 } { 8 } } - \frac { 11 } { 18 }$$

Evaluate

$$\frac{\sqrt{2}-2}{4}\approx -0.146446609$$

Solution Steps

Subtract \frac{2}{3} from 1 to get \frac{1}{3}.

$$\left(\frac{1}{3}\right)^{2}+\sqrt{1-\frac{7}{8}}-\frac{11}{18}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}+\sqrt{1-\frac{7}{8}}-\frac{11}{18}$$

Subtract \frac{7}{8} from 1 to get \frac{1}{8}.

$$\frac{1}{9}+\sqrt{\frac{1}{8}}-\frac{11}{18}$$

Rewrite the square root of the division \sqrt{\frac{1}{8}} as the division of square roots \frac{\sqrt{1}}{\sqrt{8}}.

$$\frac{1}{9}+\frac{\sqrt{1}}{\sqrt{8}}-\frac{11}{18}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{9}+\frac{1}{\sqrt{8}}-\frac{11}{18}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{1}{9}+\frac{1}{2\sqrt{2}}-\frac{11}{18}$$

Rationalize the denominator of \frac{1}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1}{9}+\frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\frac{11}{18}$$

The square of \sqrt{2} is 2.

$$\frac{1}{9}+\frac{\sqrt{2}}{2\times 2}-\frac{11}{18}$$

Multiply 2 and 2 to get 4.

$$\frac{1}{9}+\frac{\sqrt{2}}{4}-\frac{11}{18}$$

Subtract \frac{11}{18} from \frac{1}{9} to get -\frac{1}{2}.

$$-\frac{1}{2}+\frac{\sqrt{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply -\frac{1}{2} times \frac{2}{2}.

$$-\frac{2}{4}+\frac{\sqrt{2}}{4}$$

Since -\frac{2}{4} and \frac{\sqrt{2}}{4} have the same denominator, add them by adding their numerators.

$$\frac{-2+\sqrt{2}}{4}$$

Factor

$$\frac{\sqrt{2} - 2}{4} = -0.1464466094067262$$